Taylor expansions for continuous Stieltjes differential equations

Abstract

The general structure of Taylor expansions of functions of solutions of continuous Stieltjes differential equations is established. A compact formalism involving hierarchical sets of multi-indices and their associated remainder sets is used. The corresponding multiple Riemann-Stieltjes integrals of time and of the driving functions in the Stieltjes terms of the differential equations, necessarily of bounded variation and continuous here, appear in the expansions and their remainders.